Stability Annealing Selects the Implicit Bias of Smoothed Sign Descent: A Rate-Indexed Barrier Path on Separable Data
Adaptive gradient methods can favor max-margin separators that differ from gradient descent, yet a fixed positive numerical stability constant eventually changes the update geometry again. This paper studies the rate-controlled middle case for full-batch linear classification on separable data. For memoryless stability-annealed smoothed-sign descent with weighted exponential loss, we prove that the normalized iterates converge to the minimizer of a convex Burg-type barrier over a margin slice. The proof rewrites the dynamics exactly as entropic mirror ascent on a concave dual objective, controls the dual gap by a KL recursion, and yields an explicit S_t^{-1/2} normalized-iterate envelope....
| Authors | Xiangwu Wang, Chengwei Cao, Yicheng Song et al. |
|---|---|
| Primary category | cs.LG |
| Published | 7 July 2026 |
| Last updated at source | 7 July 2026 |
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